Our calculations were performed using density functional theory (DFT) as implemented in the Vienna ab initio simulation package (VASP) code [1]}, [2]}, [3]}. The generalized-gradient approximation (GGA) for the exchange correlation functional was used. Throughout the work, the cutoff energy was set to be 550 eV for expanding the wave functions into plane-wave basis. In the calculation, the Brillouin zone was sampled in the \(k\)  space within Monkhorst-Pack scheme [4]}. On the basis of the equilibrium structure, the \(k\)  mesh used was \(10\times 10\times 6\) . The intrinsic Hall conductivity \(\sigma _{xy}^{int}\)  is obtained by integrating the \(z\)  component of Berry curvature \(\Omega _{xy}^z(\textbf {k})\)  on all the occupied states through the Brillouin zone with SOC included and the moment of Mn along \(z\)  axis.
